scholarly journals Necessary and sufficient conditions for functions involving the psi function to be completely monotonic

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Zhen-Hang Yang ◽  
Yu-Ming Chu ◽  
Xiao-Hui Zhang
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Psi Function ◽  
Completely Monotonic ◽  
Necessary And Sufficient

scholarly journals COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE DIVIDED DIFFERENCE OF PSI FUNCTIONS

2013 ◽  
Vol 88 (2) ◽  
pp. 309-319 ◽  
Author(s):  
FENG QI ◽  
PIETRO CERONE ◽  
SEVER S. DRAGOMIR
Keyword(s):  
Divided Difference ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Complete Monotonicity ◽  
Divided Differences ◽  
Psi Function ◽  
Gamma Functions ◽  
Completely Monotonic ◽  
Polygamma Functions ◽  
Necessary And Sufficient

AbstractNecessary and sufficient conditions are presented for a function involving the divided difference of the psi function to be completely monotonic and for a function involving the ratio of two gamma functions to be logarithmically completely monotonic. From these, some double inequalities are derived for bounding polygamma functions, divided differences of polygamma functions, and the ratio of two gamma functions.

scholarly journals Monotonicity and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function

2020 ◽  
Author(s):  
Feng Qi
Keyword(s):  
Sufficient Conditions ◽  
Laplace Transforms ◽  
Necessary And Sufficient Conditions ◽  
Complete Monotonicity ◽  
Convolution Theorem ◽  
Monotonic Functions ◽  
Completely Monotonic ◽  
Completely Monotonic Functions ◽  
Necessary And Sufficient ◽  
Derivatives Of

In the paper, by convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein's theorem for completely monotonic functions, and other analytic techniques, the author (1) presents the decreasing monotonicity of a ratio constituted via three derivatives of a function involving trigamma function; (2) discovers necessary and sufficient conditions for a function constituted via three derivatives of a function involving trigamma function to be completely monotonic. These results conform previous guesses posed by the author.

scholarly journals Necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic

2020 ◽  
Author(s):  
Feng Qi
Keyword(s):  
Exponential Function ◽  
Sufficient Conditions ◽  
Laplace Transforms ◽  
Necessary And Sufficient Conditions ◽  
Convolution Theorem ◽  
Completely Monotonic ◽  
Necessary And Sufficient ◽  
Derivatives Of

In the paper, by convolution theorem for the Laplace transforms, some properties of a function involving exponential function, and other analytic techniques, the author finds necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic.

scholarly journals Complete monotonicity of a difference constituted by four derivatives of a function involving trigamma function

2020 ◽  
Author(s):  
Feng Qi
Keyword(s):  
Sufficient Conditions ◽  
Laplace Transforms ◽  
Necessary And Sufficient Conditions ◽  
Complete Monotonicity ◽  
Convolution Theorem ◽  
Monotonic Functions ◽  
Completely Monotonic ◽  
Completely Monotonic Functions ◽  
Necessary And Sufficient ◽  
Derivatives Of

In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein's theorem for completely monotonic functions, and other techniques, the author finds necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic.

scholarly journals Necessary and sufficient conditions for complete monotonicity and monotonicity of two functions defined by two derivatives of a function involving trigamma function

2021 ◽  
pp. 14-14
Author(s):  
Feng Qi
Keyword(s):  
Exponential Function ◽  
Sufficient Conditions ◽  
Laplace Transforms ◽  
Necessary And Sufficient Conditions ◽  
Complete Monotonicity ◽  
Monotonic Functions ◽  
Completely Monotonic ◽  
Completely Monotonic Functions ◽  
Necessary And Sufficient ◽  
Derivatives Of

In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein's theorem for completely monotonic functions, some properties of a function involving exponential function, and other analytic techniques, the author finds necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic. These results generalize corresponding known ones.

scholarly journals Complete monotonicity of divided differences of the di- and tri-gamma functions with applications

2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Feng Qi ◽  
Bai-Ni Guo
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Complete Monotonicity ◽  
Divided Differences ◽  
Gamma Functions ◽  
Completely Monotonic ◽  
Polygamma Functions ◽  
Necessary And Sufficient

AbstractIn the paper, we establish necessary and sufficient conditions for two families of functions involving divided differences of the di- and tri-gamma functions to be completely monotonic. Consequently, we derive necessary and sufficient conditions for two families of functions involving the ratio of two gamma functions to be logarithmically completely monotonic. Furthermore, we deduce some inequalities for bounding the ratio of two gamma functions and divided differences of polygamma functions.

scholarly journals Monotonicity of a ratio involving trigamma and tetragamma functions

2020 ◽  
Author(s):  
Feng Qi
Keyword(s):  
Sufficient Conditions ◽  
Laplace Transforms ◽  
Necessary And Sufficient Conditions ◽  
Exponential Functions ◽  
Monotonic Functions ◽  
Completely Monotonic ◽  
Completely Monotonic Functions ◽  
The Right ◽  
Necessary And Sufficient ◽  
Logarithmic Concavity

In the paper, by convolution theorem of the Laplace transforms, Bernstein's theorem for completely monotonic functions, and logarithmic concavity of a function involving exponential functions, the author(1) finds necessary and sufficient conditions for a ratio involving trigamma and tetragamma functions to be monotonic on the right real semi-axis;(2) and presents alternative proofs of necessary and sufficient conditions for a function and its negativity involving trigamma and tetragamma functions to be completely monotonic on the positive semi-axis.These results generalizes known conclusions recently obtained by the author.

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